It is possible but the real question you need to ask yourself is "wouldn't a blog or a website achieve the same thing?" You could write "messages" in that blog/website and it will remain on the internet for a very long time so that people in the future can read what you wrote.
The difference however is that a blog/website is designed to "store messages" while bitcoin blockchain is not.
I get the impression that the OP wants to store a message that he can prove is unchanged.
Depending on why OP need to prove it's unchanged, website archive service is good enough. An example,
.